What does marginalization refer to in Bayesian inference?

Marginalization in Bayesian inference refers to the process of integrating out variables to focus on a subset of variables. This is an essential concept because it allows researchers and practitioners to simplify complex models by reducing the dimensionality of the data they are working with. By marginalizing over unwanted or latent variables, one can obtain the marginal distribution of the parameters of interest.

For example, if you are trying to understand the relationship between two variables but there are additional, possibly confounding variables in your model, marginalization allows you to derive the distribution of the two variables by integrating over the distributions of the confounding variables. This enables us to make predictions or infer probabilities concerning our variables of interest without the distractions or complexities added by those other variables.

The other options touch on various aspects of statistical analysis but do not accurately represent the concept of marginalization in the context of Bayesian inference. Eliminating irrelevant data from a dataset does not capture the essence of integrating variables. Calculating probabilities in frequentist statistics is a different paradigm altogether and does not involve marginalization. Lastly, while comparing different statistical models can be part of the modeling process, it does not describe marginalization, which specifically pertains to the handling of variables within a model.